Estimated distance calculator, estimated distance calculation method, estimated distance calculation program, and automated planner

ABSTRACT

An estimated distance calculator  10  generates, on the basis of a first state element model comprising multiple state elements, a second state element model which is another state element model, wherein the state elements include multiple states and state transitions assigned with transition conditions between the multiple states. The calculator includes a generation unit  11  which generates the second state element model in such a manner as to comprise any one state element among the multiple state elements and state elements other than the one state element which are selected from among the multiple state elements after transition conditions satisfying predetermined condition are removed.

TECHNICAL FIELD

The present invention relates to an estimated distance calculator, anestimated distance calculation method, an estimated distance calculationprogram, and an automated planner, more particularly to an estimateddistance calculator, an estimated distance calculation method, anestimated distance calculation program, and an automated planner for usein solving automated planning problems to allow an autonomous controlsystem including artificial intelligence to decide a procedure forexecuting actions and tasks.

BACKGROUND ART

The automated planning is an art of scheduling actions, for example,action to be taken next, using artificial intelligence based on knownenvironmental information. Among the known automated planning methods isa method of solving a shortest path problem, i.e., searching and findinga shortest path on a diagram representing the transition relationship ofone state to another. The shortest path problem may be hereinafterreferred to as automated planning problem.

FIG. 34 is an explanatory diagram showing an example of a state diagram.This state diagram shows a relationship among transitions betweenstates.

Circles showed in FIG. 34 each represent a state. As showed in FIG. 34,one of the circles represents a current state, and the other circlerepresents a target state. In FIG. 34, arrows drawn between the circleseach represent a transition relationship of one state to another. Thestate diagram of FIG. 34 indicates that the state transitions indicatedwith the arrows are possible.

Notations of the current state and target state may be similarly drawnin any other drawings.

The shortest path problem solving method defines a current state and atarget state in a state diagram, like the one showed in FIG. 34,searches possible routes of transition of the current state to thetarget state along the arrows, and calculates and obtains, among thesearched routes, a route representing the shortest procedure to arriveat the target state.

PTL 1 describes how to output a system updating procedure using theautomated planning. Specifically, PTL 1 describes an automated planningproblem solving method. In this method, calculating the shortestprocedure of updating one large system including a plurality of smallstate transition systems that depend on other state transition systemsis defined as calculating the shortest path on a state diagram toconsequently solve the automated planning problem.

NPL 1 describes A* search which is one of solutions to the shortest pathproblem. In the A* search, states on the state diagram are marked withscores in search of the shortest path on the diagram while tracing thestates.

The scores given to the states in the A* search are values calculatedfrom [“distance from current state to search state”+“estimated distancefrom search state to target state”]. The A* search marks the states withscores and defines the states with lower scores to be nearer to thetarget state, based on which the lower-scored states are searched withhigher priority.

FIG. 35 is an explanatory diagram showing a specific example of the A*search of a shortest path. As showed in FIG. 35, states painted in blackare search states. Hatched states have already been searched. Stateswith numbers are states with scores.

FIG. 35 show search results in different stages of the shortest pathsearch by the A* search (hereinafter, search phases). In the A* search,the search state is initially as the current state, as showed in upperleft of FIG. 35. Then, the A* search calculates the scores of all of thestates adjacent to the search state.

After the scores are calculated, the A* search causes transition of thesearch state to a state with the lowest score among all of the statesyet to be searched whose scores are already known (unsearched state).The A* search repeatedly carries out these steps until the search statefinally arrives at the target state in order to obtain the shortestpath.

The unsearched states with scores already known in the search phase ofupper right of FIG. 35 have scores of 3, 4, 4, and ∞. The A* searchcauses transition of the search state to an unsearched state with thelowest score “3”. The lower left of FIG. 35 shows a search result in anext phase to the search phase of upper right of FIG. 35 subsequent tothe search state transition. The lower right of FIG. 35 shows a searchresult in the final search phase.

The description of the examples showed in FIG. 35, however, fails toclearly identify any specific method of calculating “an estimateddistance from the search state to the target state”. When a methodcurrently employed to calculate the estimated distance is changed, howto proceed with search may accordingly change.

A function for estimation of a distance to a target state is referred toas heuristic function. It is a known matter that an estimated distancemust be always less than a true distance in order to obtain a correctshortest path using the A* search. It is also a known matter that anestimated distance is preferably as closer to a true distance aspossible for a higher search speed in the A* search.

The A* search, without relying on the heuristic function, may always setthe estimated distance to “0” to search the shortest path. The A* searchalways using the estimated distance set to “0” may be performedsimilarly to the search method called “Dijkstra's algorithm”.

A known method of formulating a good heuristic function is to build arelaxed problem(s). PTL 2 describes an exemplified art of using aheuristic function built by formulating the relaxed problem.Specifically, PTL 2 describes a method of dividing a loading problem; atask of reloading multiple items, into a few relaxed problems.

CITATION LIST Patent Literature

-   PTL 1: US Patent Application Publication No. 2015/0324211-   PTL 2: Japanese Patent Application Laid-Open No. 2014-055037

Non Patent Literature

-   NPL 1: Peter E. Hart, Nils J. Nilsson, and Bertram Raphael, “A    Formal Basis for the Heuristic Determination of Minimal Cost Paths,”    in IEEE Transactions on Systems Science and Cybernetics, vol. 4, no.    2, pp. 100-107, July 1968.

SUMMARY OF INVENTION Technical Problem

First, an automated planning problem, which is assumed to be processedby the present invention, is hereinafter described to address thetechnical issues.

The automated planning problem to be processed by the present inventionis a planning problem similar to the automated planning problemdescribed in PTL 1 and is aimed at obtaining a shortest path on a modelwhere state diagrams are arranged. In the description given below, astate element model refers to a model where state diagrams are arranged,and a state element refers to a state diagram constituting the stateelement model.

A specific example of the automated planning problem is described below.FIG. 36 is an explanatory diagram showing initial states and targetstates of a crane and a load. The initial state showed in FIG. 36indicates that the crane and the load are both at a location A. Thetarget state showed in FIG. 36 indicates that the crane is currently atthe location A, and the load at a location B.

An automated planning problem is generated in order to obtain a shortestprocedure for transition of the initial state to the target state asshowed in FIG. 36. FIG. 37 is an explanatory diagram showing an exampleof a state element model. The state element model showed in FIG. 37 ispresented by the generated automated planning problem.

A state element “item” and a state element “crane” are arranged on thestate element model showed in FIG. 37. The state element “item” is thestate element of the load showed in FIG. 36. The state element “crane”is the state element of the crane showed in FIG. 36.

The state element “item” showed in FIG. 37 includes a state A, a state“picked”, and a state B. The state A indicates that the load iscurrently at the location A. The state “picked” indicates that the loadis held by the crane. The state B indicates that the load is currentlyat the location B.

The state element “crane” showed in FIG. 37 includes a state A and astate B. The state A indicates that the crane is currently at thelocation A. The state B indicates that the crane is currently at thelocation B.

In the state element “item” in FIG. 37, the state A is set as thecurrent state, and the state B is set as the target state on the basisof FIG. 36. In the state element “crane” in FIG. 37, the state A is setas the current state and the target state both.

In the state element model are also described details of interferencebetween the state elements. In FIG. 37, balloons painted in black witharrows indicative of state transitions show details of interferencebetween the state elements (hereinafter, referred to as dependency).

As showed in FIG. 37, the balloons each contain the name of the otherstate element and a set of states included in the state elementindicated by the name. Each balloon indicates that state transition withthe balloon is left undone unless the state element indicated by thename written in the balloon has any state included in the set of states.

For example, the dependency showed in FIG. 37, [crane: {A}], isassociated with state transitions of the state element “item”; stateA→state “picked”, and state “picked” →state A. This means that neitherof state transitions of the state element “item”; state A→state“picked”, and state “picked” →state A, is not allowed unless the state Ais the state of the state element “crane”.

The automated planning problem that seeks a shortest path on the stateelement model showed in FIG. 37 is comparable to a problem that seeks ashortest procedure of carrying the load at the location A to thelocation B using the crane showed in FIG. 36. The automated planningproblem that seeks a shortest path on the state element model iseventually a problem that seeks a shortest procedure for statetransitions of all of the state elements to their target states.

FIG. 38 is a drawing that shows an example of changes of state elementsof a crane and a load when the load currently at the location A iscarried to the location B by the crane according to a shortestprocedure. FIG. 38 is an explanatory diagram showing an example ofchanges in a state element model. In FIG. 38, search states painted inblack represent states of the crane and the load in different stages.

As showed in the first dashed rectangle from the left of FIG. 38, thecrane and the load at the location A in an initial stage are both in thestate A. The load is then held by the crane in a stage that follows, atwhich state transition of the load to the state “picked” occurs, asshowed in the second dashed rectangle from the left of FIG. 38. Thecrane holding the load then moves from the location A to the location B,and state transition of the crane to the state B occurs, as showed inthe third dashed rectangle from the left of FIG. 38.

The crane that moved to the location B then releases the load,therefore, state transition of the load to the state B occurs, arrivingat the target state, as showed in the fourth dashed rectangle from theleft of FIG. 38. The crane that released the load then moves from thelocation B to the location A, therefore, state transition of the craneto the state A occurs, arriving at the target state, as showed in thefifth dashed rectangle from the left of FIG. 38. Thus, the solution tothe automated planning problem is the procedure showed in a lower partof FIG. 38.

It is contemplated to calculate a shortest path on a state element modelin which all of state elements arrive at their target states, as showedin FIG. 38. When the algorithm described in PTL 1 is used, the stateelement model showed in FIG. 37 is laid out in a state diagram showed inFIG. 39. The present invention defines this state diagram as “globalstate diagram”. The present invention further defines statesconstituting the global state diagram as “global states”.

FIG. 39 is an explanatory diagram showing an example of the global statediagram. In FIG. 39, similarly to states included in state elements, aglobal state with an arrow directed rightward is the current state, anda global state in a double-lined box is the target state.

The current state and target state in the global state diagram depend oncombinations of the state elements. Specifically, the state of the stateelement model in which states of all of the state elements are thecurrent state is the current state in the global state diagram(hereinafter, global current state). Specifically, the state of thestate element model in which state transitions of all of the stateelements to their target states are completed is the target state in theglobal state diagram (hereinafter, global target state).

The automated planning problem that seeks the shortest path on the stateelement model is comparable to a problem that seeks a shortest procedurefor transition of the global state from the global current state to theglobal target state in the global state diagram into which the stateelement model has been converted. This means that the procedure showedin FIG. 38 is obtained by solving the problem that seeks the shortestpath on the global state diagram showed in FIG. 39.

The method described in PTL 1 may succeed in solving the automatedplanning problem that seeks the shortest path on the state elementmodel. Yet, there is an issue to be addressed with the method describedin PTL 1, which is described below.

The issue that remains unsolved in the method described in PTL 1 isexponential increase of a state space in proportion to a greater numberof state elements included in the state element model, which mayexponentially increase calculation time required to solve the automatedplanning problem.

When a state element including “n” number of states is added to thestate element model, for example, the number of global statesconstituting the global state diagram into the state element model hasbeen converted is “n” times greater than before the state element isadded.

When, for example, 10 new state elements including three states areadded to the state element model, the number of global statesconstituting the global state diagram is 3¹⁰=59,049 times greater thanbefore the state elements are added.

Supposing that calculation time required to search the shortest path issimply proportional to the number of global states constituting theglobal state diagram, additional 10 new state elements may result inapproximately 59,049 times longer calculation time. Considering theprospect of future increase of state elements to be included in a stateelement model to, for example, 20, 30, or more, solving the automatedplanning problem using the known art alone strongly suggests thepossibility of searches being unfinished within realistic time spans.

Unless any heuristic function suitable for the A* search is introduced,such a drastic increase of calculation time may be likely to occur inproblems with use cases for which the automated planning problem may beconsidered relatively useful. A specific example of drasticallyincreased calculation time is described referring to FIG. 40.

FIG. 40 is an explanatory diagram showing another example of the stateelement model. FIG. 40 shows a specific example of the state elementmodel in which execution time for the shortest path searching processsignificantly increases when no heuristic function is used.

The state element model showed in FIG. 40 includes a state element“App1”, a state element “App2”, a state element “App3”, and a stateelement “Conf”. FIG. 40 shows a state element model representing asystem including three applications and a configuration file sharedamong the applications.

The state elements “App1”, “App2”, and “App3” are state elementsrespectively corresponding to an application 1, an application 2, and anapplication 3. As showed in FIG. 40, each application is modeled into astate element including two states; state “on” indicative of “currentlyoperating”, and state “off” indicative of “currently suspended”.

The state element “Conf” is a state element corresponding to theconfiguration file. As showed in FIG. 40, the configuration file ismodeled into a state element including two states; state “old”indicative of “before updating”, and state “new” indicative of “afterupdating”.

Updating the configuration file in the example of FIG. 40 is discussedbelow. In case the configuration file is to be updated, the currentstate of the state element “Conf” is the state “old”, and the targetstate is the state “new”, as showed in FIG. 40. As for the stateelements “App1” to “App3”, their current and target states are both thestate “on”.

As showed in FIG. 40, dependency [App1:{off}, App2:{off}, App3{off}] isassociated with state transition, state “old”→state “new”, of the stateelement “Conf”. The reason for that is, if the configuration file isupdated while an applications is active, the application may fail tocorrectly read data. Therefore, state transition, state “old”→state“new”, of the state element “Conf” corresponding to the configurationfile does not occur unless all of the applications referring to theconfiguration file are inactive.

The global states including states of the state elements “App1” to“App3” are expressed as [(“App1” state), (“App2” state), (“App3”state)]. When the A* search searches a shortest procedure of updatingthe configuration file in the global states without calculating theirscores, the global states are searched in the order of [on, on, on],[on, on, off], [on, off, on], [off, on, on], [on, off, off], [off, on,off], [off, off, on], and [off, off, off].

The reason for that is, if scores are unused, the A* search may proceedwith the global states near to the global current state. In order toobtain a shortest procedure for state transition of the state element“Conf” from the state “old” to the state “new”, the A* search isrequired to search all of the global states present between the globalcurrent state and the most remote global target state [off, off, off].

In the case of an optionally increased number of applications asdescribed earlier, the search of a shortest path between the currentstate and the most remote state may be requested. To calculate ashortest path on a state element model representing a system including“n” number of applications, for example, 2^(n) number of states, atmost, may have to be searched to continue the search to all of theapplications are turned off. This means that calculation time requiredfor the shortest path search exponentially increases with a greaternumber of applications included in the system.

When the A* search is used to search a shortest path on a state elementmodel including abundant state elements, therefore, a suitable heuristicfunction is importantly selected. Therefore, an apparatus for use insolving the automated planning problem is desirably obtained thatenables high-speed search of a shortest path, even under suchcircumstances, by estimating a shortest distance to the target stateusing a suitable heuristic function on the basis of dependency betweenthe state elements.

Purpose of Invention

To address the issues of the known art, the present invention providesan estimated distance calculator, an estimated distance calculationmethod, an estimated distance calculation program, and an automatedplanner that may successfully enable high-speed search of a shortestpath on a state element model.

Solution to Problem

The present invention provides an estimated distance calculator thatgenerates, on the basis of a first state element model comprisingmultiple state elements, a second state element model which is anotherstate element model, wherein the state elements include multiple statesand state transitions assigned with transition conditions between themultiple states. The estimated distance calculator includes a generationunit which generates the second state element model in such a manner asto comprise any one state element among the multiple state elements andstate elements other than the one state element which are selected fromamong the multiple state elements after transition conditions satisfyingpredetermined condition are removed.

The present invention provides an estimated distance calculation methodusable in an estimated distance calculator that generates, on the basisof a first state element model comprising multiple state elements, asecond state element model which is another state element model, whereinthe state elements include multiple states and state transitionsassigned with transition conditions between the multiple states. Theestimated distance calculation method includes generating the secondstate element model in such a manner as to comprise any one stateelement among the multiple state elements and state elements other thanthe one state element which are selected from among the multiple stateelements after transition conditions satisfying predetermined conditionare removed.

The present invention provides an estimated distance calculation programexecutable in a computer that generates, on the basis of a first stateelement model comprising multiple state elements, a second state elementmodel which is another state element model, wherein the state elementsinclude multiple states and state transitions assigned with transitionconditions between the multiple states. The estimated distancecalculation program prompts the computer to execute a processing step ofgenerating the second state element model in such a manner as tocomprise any one state element among the multiple state elements andstate elements other than the one state element which are selected fromamong the multiple state elements after transition conditions satisfyingpredetermined condition are removed.

The present invention provides an automated planner that generates, onthe basis of a first state element model comprising multiple stateelements, a second state element model which is another state elementmodel, wherein the state elements include multiple states and statetransitions assigned with transition conditions between the multiplestates. The automated planner includes a generator, an elicitor, and asearcher. The generator generates the second state element model in sucha manner as to comprise any one state element among the multiple stateelements and state elements other than the one state element which areselected from among the multiple state elements after transitionconditions satisfying predetermined condition are removed. The elicitorreceives, as input, the second state element model and that elicits, onthe basis of a current state and a target state included in the secondstate element model, a smallest number of transitions for the currentstate to arrive at the target state. The searcher searches, using thesmallest number of transitions, a shortest path which is a solution toan automated planning problem expressed by the first state elementmodel.

Advantageous Effects of Invention

The present invention may enable a high-speed search of a shortest pathon a state element model.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing a configuration example of a firstexemplary embodiment of an estimated distance calculator 100 accordingto the present invention.

FIG. 2 is a flowchart showing an operation of a relaxed problemgenerating process performed by a constraint relaxing unit 101.

FIG. 3 is an explanatory diagram showing an example of the relaxedproblem generating process performed by the constraint relaxing unit101.

FIG. 4 is a flowchart showing an operation of an estimated distancecalculating process performed by a solving unit 102.

FIG. 5 is an explanatory diagram showing an example of relaxed problemgenerated by the constraint relaxing unit 101.

FIG. 6 is an explanatory diagram showing an example of the estimateddistance calculating process performed by the solving unit 102.

FIG. 7 is an explanatory diagram showing an example of a shortest pathsearching process using breadth first search simulation.

FIG. 8 is a block diagram showing a configuration example of a secondexemplary embodiment of an estimated distance calculator 110 accordingto the present invention.

FIG. 9 is a flowchart showing an operation of an estimated distancecalculating process performed by a solving unit 112.

FIG. 10 is a flowchart showing an operation of a transition array lengthcalculating process performed by the solving unit 112.

FIG. 11 is an explanatory diagram showing an example of the transitionarray length calculating process performed by the solving unit 112.

FIG. 12 is a block diagram showing a configuration example of a thirdexemplary embodiment of an estimated distance calculator 120 accordingto the present invention.

FIG. 13 is a flowchart showing an operation of a relaxed problemgenerating process performed by a constraint relaxing unit 111.

FIG. 14 is an explanatory diagram showing an example of automatedplanning problem P inputted to the constraint relaxing unit 111.

FIG. 15 is an explanatory diagram showing an example of a dependencytree calculating process performed by the constraint relaxing unit 111.

FIG. 16 is an explanatory diagram showing another example of automatedplanning problem P inputted to the constraint relaxing unit 111.

FIG. 17 is an explanatory diagram showing an example of a dependencytree generated by the constraint relaxing unit 111.

FIG. 18 is an explanatory diagram showing an example of the relaxedproblem generating process performed by the constraint relaxing unit111.

FIG. 19 is a flowchart showing an operation of a transition array lengthcalculating process performed by a solving unit 122.

FIG. 20 is an explanatory diagram showing a relaxed problem Q inputtedto the solving unit 122 and an example of dependency tree T (E1) used togenerate the relaxed problem Q.

FIG. 21 is an explanatory diagram showing a process to calculate thedistance of the solution to the relaxed problem Q in the transitionarray length calculating process performed by the solving unit 122.

FIG. 22 is an explanatory diagram showing an example of subtreesgenerated by the solving unit 122.

FIG. 23 is an explanatory diagram showing an example of problem Q′generated by the solving unit 122.

FIG. 24 is an explanatory diagram showing an example of how the problemQ′ is solved by the solving unit 122.

FIG. 25 is a block diagram showing a configuration example of a fourthexemplary embodiment of an automated planner 200 according to thepresent invention.

FIG. 26 is a flowchart showing an operation of a shortest path searchingprocess performed by a shortest path searching unit 202.

FIG. 27 is an explanatory diagram showing a specific example of theshortest path searching process performed by the shortest path searchingunit 202.

FIG. 28 is an explanatory diagram showing a specific example of theshortest path searching process performed by the shortest path searchingunit 202.

FIG. 29 is an explanatory diagram showing another example of a stateelement model.

FIG. 30 is an explanatory diagram showing another example of a stateelement model.

FIG. 31 is an explanatory diagram showing an example of a hardwareconfiguration of the estimated distance calculator according to thepresent invention.

FIG. 32 is a block diagram schematically showing the estimated distancecalculator according to the present invention.

FIG. 33 is a block diagram schematically showing the automated planneraccording to the present invention.

FIG. 34 is an explanatory diagram showing an example of a state diagram.

FIG. 35 is an explanatory diagram showing a specific example of the A*search of a shortest path.

FIG. 36 is an explanatory diagram showing initial states and targetstates of a crane and a load.

FIG. 37 is an explanatory diagram showing an example of a state elementmodel.

FIG. 38 is an explanatory diagram showing an example of changes in astate element model.

FIG. 39 is an explanatory diagram showing an example of a global statediagram.

FIG. 40 is an explanatory diagram showing another example of a stateelement model.

DESCRIPTION OF EXEMPLARY EMBODIMENTS First Exemplary Embodiment

[Description of Structure]

Exemplary embodiments of the present invention are hereinafter describedreferring to the accompanying drawings. FIG. 1 is a block diagramshowing a configuration example of a first exemplary embodiment of anestimated distance calculator 100 according to the present invention.

The estimated distance calculator 100 showed in FIG. 1 receives, asinput, an automated planning problem for search of a shortest path on astate element model. The estimated distance calculator 100 outputs anestimated distance of the shortest path from a current state to a targetstate on the state element model indicated by the automated planningproblem.

The estimated distance calculator 100 according to this exemplaryembodiment, using a method of estimating distances between differentstates by taking into account dependency constraints in the stateelement model, allows a shortest path searching device (not showed inthe drawings) to perform a high-speed A* search on a global statediagram. The estimated distance calculator 100 according to thisexemplary embodiment may quickly solve the automated planning problemthat seeks the shortest path on the state element model.

As showed in FIG. 1, the estimated distance calculator 100 according tothis exemplary embodiment has a constraint relaxing unit 101 and asolving unit 102.

The constraint relaxing unit 101 has a function to relax the inputtedautomated planning problem. The constraint relaxing unit 101 removesdependency included in any state element but one of a plurality of stateelements constituting the state element model indicated by the automatedplanning problem and thereby relaxes the automated planning problem togenerate a relaxed problem.

The constraint relaxing unit 101 inputs the generated relaxed problem tothe solving unit 102. The solving unit 102 has a function to calculatesolutions to the inputted relaxed problem. The solutions to the relaxedproblem are to find a shortest path on the state element model indicatedby the relaxed problem. The solving unit 102 outputs a most suitable oneof the solutions to the relaxed problem as an estimated distance of theshortest path on the state element model indicated by the automatedplanning problem.

[Description of Operation]

The operation to output the estimated distance obtained by the estimateddistance calculator 100 according to this exemplary embodiment ishereinafter described referring to FIGS. 2 and 4.

The description starts with a relaxed problem generating processperformed by the constraint relaxing unit 101. FIG. 2 is a flowchartshowing an operation of the relaxed problem generating process performedby the constraint relaxing unit 101.

After an automated planning problem P that seeks a shortest path on thestate element model M is inputted to the estimated distance calculator100, the automated planning problem P is inputted to the constraintrelaxing unit 101 (step S110). Then, the constraint relaxing unit 101defines a set R as void set (empty set) (step S111).

Next, the constraint relaxing unit 101 retrieves, out of the stateelements included in the state element model M, a state element E forwhich any relaxed problem Q relevant to itself is yet to be generated.This means that the operation enters a relaxed problem generating loop(step S112).

The constraint relaxing unit 101 generates the relaxed problem Qrelevant to the retrieved state element E (step S113). Morespecifically, the constraint relaxing unit 101 generates the relaxedproblem Q relevant to the state element E by deleting, from dependenciesincluded in the state element model M, all of dependencies butdependencies associated with state transitions involved with the stateelement E.

Next, the constraint relaxing unit 101 redefines the set R as a set towhich the relaxed problem Q has been added (step S114). This means thatthe constraint relaxing unit 101 adds the relaxed problem Q generated instep S113 to the elements of the set R.

The constraint relaxing unit 101 repeatedly executes steps S113 and S114for any state element E for which any relaxed problem Q relevant toitself is yet to be generated among the state elements included in thestate element model M. Steps S113 and S114 are repeatedly performed foreach and all of the state elements included in the state element modelM.

After the relaxed problems Q relevant to all of the state elementsincluded in the state element model M are generated, the constraintrelaxing unit 101 exits the relaxed problem generating loop (step S115).The constraint relaxing unit 101 that exited the relaxed problemgenerating loop outputs the set R (step S116). After the output of theset R, the constraint relaxing unit 101 ends the relaxed problemgenerating process.

FIG. 3 is an explanatory diagram showing an example of the relaxedproblem generating process performed by the constraint relaxing unit101. The state element model M showed in FIG. 3 includes a state elementE1, a state element E2, and a state element E3.

The constraint relaxing unit 101 uses the relaxed problem generatingprocess to relax the automated planning problem P that seeks theshortest path on the state element model M. More specifically, theconstraint relaxing unit 101, when relaxing the automated planningproblem P in connection with the state element E1, generates a relaxedproblem Q1 from which all of dependencies but dependencies associatedwith state transitions involved with the state element E1 have beendeleted, as showed in FIG. 3.

Similarly, the constraint relaxing unit 101 generates relaxed problemsQ2 and Q3 to relax the automated planning problem P in connection withthe state elements E2 and E3. As showed in FIG. 3, when the automatedplanning problem P indicates the state element model M including threestate elements, the constraint relaxing unit 101 generates three relaxedproblems using the relaxed problem generating process.

Next, an estimated distance calculating process performed by the solvingunit 102 is hereinafter described. FIG. 4 is a flowchart showing anoperation of an estimated distance calculating process performed by asolving unit 102.

First, a set R of relaxed problems Q outputted by the constraintrelaxing unit 101 is inputted to the solving unit 102 (step S120). Then,the solving unit 102 sets SCORE2 to 0 (step S121).

Then, the solving unit 102 retrieves the relaxed problem Q yet to besolved from the relaxed problems Q included in the set R. This meansthat the operation enters an estimated distance calculating loop (stepS122).

The solving unit 102 solves the retrieved relaxed problem Q within theestimated distance calculating loop. In this description, $Q hereinafterrefers to any state element still including dependency among the stateelements included in the relaxed problem Q. Further, it hereinafterrefers to a non-redundant path for state transition of the state element$Q from the current state to the target state.

On the other hand, “redundant path” may refer to a path in whichtransition of a search state to the same state occurs twice. Forexample, a path “a₁→c₁→a₁→b₁→c₁” is a redundant path involving twotransitions of the search state to a₁ and to c₁.

First, the solving unit 102 sets SCORE1 to ∞ (step S123). Then, thesolving unit 102 decides a path π whose transition array is yet to beobtained. This means that the operation enters a shortest path searchingloop (step S124).

A state transition of the state element $Q included in the relaxedproblem Q along the shortest path on the global state diagram maypossibly be a transition along a certain non-redundant path π. In thisexemplary embodiment, the solving unit 102 solves the relaxed problem Q,assuming that “state transition of the state element $Q occurs along thepath π”.

Before the state element $Q presently in the current state finallyarrives at the target state, there is more than one state transition.The solving unit 102 obtains, as the solution to the relaxed problem Q,a transition array of state transitions arranged in the order that theyoccurred by the time when the state element $Q in the current statearrives at the target state (step S125). An example of the transitionarray is the state transition array showed at the bottom of FIG. 38,“item: A→picked, crane: A→B, item: picked→B, crane: B→A”.

Next, the solving unit 102 sets the length of the transition arrayobtained in step S125 to SCORE[π] (step S126). For instance, “4” is thelength of a transition array including four state transitions.

Then, the solving unit 102 determines whether SCORE1 is greater thanSCORE[π] (step S127). When SCORE1 is greater than SCORE[π] (True in stepS127), the solving unit 102 sets SCORE[π] to SCORE1 (step S128).

The solving unit 102 repeatedly performs steps S125 to S128 for any pathπ for which a transition array relevant to the state element $Q is yetto be obtained. Steps S125 to S128 are repeatedly performed for each andall of the paths π assumed to be non-redundant in connection with thestate element $Q.

After the transition arrays of all of the paths π relevant to the stateelement $Q are obtained, the solving unit 102 exits the shortest pathsearching loop (step S129). At the time of the solving unit 102 exitingthe shortest path searching loop, the smallest value of lengths of theobtained transition arrays is stored in SCORE1. Specifically, SCORE1 atthe time of the solving unit 102 exiting the shortest path searchingloop is a distance as the solution to the relaxed problem Q (shortestpath).

Then, the solving unit 102 determines whether SCORE1 is greater thanSCORE2 (step S130). When SCORE1 is greater than SCORE2(True in stepS130), the solving unit 102 sets SCORE1 to SCORE2 (step S131).

The solving unit 102 repeatedly performs steps S123 to S131 for anyrelaxed problem Q included in the set R whose solution is yet to befound. Steps S123 to S131 are repeatedly performed for each and all ofthe relaxed problems Q included in the set R.

When the solutions to all of the relaxed problems Q included in the setR are finally obtained, the solving unit 102 exits the estimateddistance calculating loop (step S132). At the time of the solving unit102 exiting the estimated distance calculating loop, the largest valueof distances in the solutions to the relaxed problems Q is stored inSCORE2. Specifically, SCORE2 at the time of the solving unit 102 exitingthe estimated distance calculating loop is an estimated distance of theshortest path as the solution to the automated planning problem P.

The solving unit 102 that exited the estimated distance calculating loopoutputs SCORE2 (step S133). After the output of SCORE2, the solving unit102 ends the estimated distance calculating process.

Next, a specific example of the estimated distance calculating processperformed by the solving unit 102 is hereinafter described. FIG. 5 is anexplanatory diagram showing an example of relaxed problem generated bythe constraint relaxing unit 101. The relaxed problem showed in FIG. 5is the relaxed problem Q1 generated in the relaxed problem generatingprocess showed in FIG. 3.

The relaxed problem Q1 is generated by relaxing constraints on theautomated planning problem P in connection with the state element E1. Inthe state element E1 included in the relaxed problem Q1, the currentstate is a₁, and the target state is c₁. For transition from the currentstate a₁ to the target state c₁, there are two non-redundant paths π,“a₁→c₁” and “a₁→b₁→c₁”.

Referring to FIG. 6 is described the estimated distance calculatingprocess performed by the solving unit 102 when the relaxed problem Q1showed in FIG. 5 is inputted. FIG. 6 is an explanatory diagram showingan example of the estimated distance calculating process performed bythe solving unit 102.

The solving unit 102 obtains, for each of the non-redundant paths π, aprocedure for transition of the state element E1 to the target statealong the path. For transition along the path “a₁→c₁”, it is firstrequired for the state element E2 to transit to a₂ in accordance withdependency. Therefore, a procedure P1100 including three steps, “E2:b₂→a₂”, “E1: a₁→c₁”, and “E2: a₂→b₂”, is obtained, as showed in FIG. 6.

The step “E2: b₂→a₂”, for example, is for transition of the stateelement E2 from b₂ to a₂. That is to say, one step corresponds to onestate transition. The final step “E2: a₂→b₂” is added for the stateelement E2 to arrive at the target state b₂.

For transition along the path “a₁→b₁→c₁”, the following transitions arenecessary in the mentioned order; transition of the state element E1from the state a₁ to b₁, transition of the state element E2 to the statea₂ in accordance with dependency, and transition of the state element E3to the state a₃. Therefore, a procedure P1101 including six steps isobtained, as showed in FIG. 6.

The solving unit 102 returns, as the solution, the length of theshortest procedure among the obtained procedures (step S129). In theexample showed in FIG. 6, the solving unit 102 returns, as the solution,“3” which is the length of the procedure P1100 for state transition ofthe state element E1 along the path “a₁→c₁”.

The shortest path, which is the solution to such a path-fixed relaxedproblem as showed in FIG. 6, may be obtained by breadth first searchsimulation. FIG. 7 is an explanatory diagram showing an example of ashortest path searching process using breadth first search simulation.

The breadth first search simulation is an algorithm used to obtain thesolution to such a path-fixed relaxed problem. In the dependency“E2:{b₂,c₂}” included in the state element E1 showed in FIG. 7 arespecified two states of the state element E2. In an initial stage of theshortest path searching process showed in FIG. 7, therefore, twotransition paths are presented; which of the state transitions should beselected.

When the breadth first search simulation is employed, the shortest oneamong the finally obtained procedures is selected. In the example showedin FIG. 7, a procedure P1200 is selected as the shortest path. Thebreadth first search simulation is a means used to find solutions topath-fixed relaxed problems. The solving unit 102 according to thisexemplary embodiment may use any other suitable means but the breadthfirst search simulation to solve such a path-fixed relaxed problem.

Description of Effect

The estimated distance calculator 100 according to this exemplaryembodiment has the constraint relaxing unit 101 and the solving unit102. The constraint relaxing unit 101 relaxes part of dependenciesincluded in a state element model to modify an automated planningproblem into a quickly-solvable relaxed problem. The solving unit 102solves the relaxed problem at high speed. The estimated distancecalculator 100 calculates an estimated distance including, as additionalfactor, dependency in connection with any state element most affected bydependency and thereby accelerates the A* search executed to solve theautomated planning problem that seeks the shortest path on the stateelement model.

The estimated distance calculator 100 according to this exemplaryembodiment may succeed in accelerating the A* search because this deviceis equipped to not only accelerate the process to score the statesduring the A* search but also calculate, as score, a value approximateto a path length which is a true solution.

The constraint relaxing unit 101 focuses on one state element includedin the state element model and deletes all of dependencies butdependencies associated with this state element of interest.

In this manner, the constraint relaxing unit 101, while taking intoconsideration part of the dependencies, generates a simpler relaxedproblem than the original automated planning problem.

In connection with all of the state elements included in the stateelement model, the solving unit 102 compares solutions to the relaxedproblems centered on the state elements. The solving unit 102 defines,as the estimated distance, one of the compared solutions showing alargest value. The estimated distance calculator 100 according to thisexemplary embodiment relaxes the dependency of a problem so as to relaxthe problem to be solved at high speed and uses the length of thesolution to the relaxed problem as the estimated distance. This device,therefore, may provide an estimated distance on which dependency-relatedimpact is reflected.

Estimating a distance to the target state may be required to solve, bysearching a shortest path using a heuristic function, an automatedplanning problem involved with a system including a plurality of smallstate diagrams that depend on other state diagrams. The estimateddistance should desirably be not affected by local solutions in thestate diagrams. In the estimated distance calculator 100 according tothis exemplary embodiment, the constraint relaxing unit 101 generatessimplified relaxed problems. Therefore, an estimated distance meetingthe requirements described above may be successfully calculated.

Second Exemplary Embodiment Description of Structure

A second exemplary embodiment of the present invention is hereinafterdescribed referring to the accompanying drawings. The second exemplaryembodiment describes an aspect provided to perform a verification methodin the first exemplary embodiment.

FIG. 8 is a block diagram showing a configuration example of a secondexemplary embodiment of an estimated distance calculator 110 accordingto the present invention. As showed in FIG. 8, the estimated distancecalculator 110 according to this exemplary embodiment has a constraintrelaxing unit 101 and a solving unit 112.

The estimated distance calculator 110 according to this exemplaryembodiment is provided with the solving unit 112, instead of the solvingunit 102 according to the first exemplary embodiment. Any otherstructural features of the second exemplary embodiment but the solvingunit 112 are similar to those of the first exemplary embodiment.

The solving unit 112, before solving the relaxed problem Q, divides astate element model indicated by the relaxed problem Q for each of stateelements E_1, E_2, . . . , E_n, other than the state element $Q,included in the relaxed problem Q. The solving unit 112 thus divides thestate element model indicated by the relaxed problem Q, and then obtainsthe length of a transition array.

Description of Operation

Next, an estimated distance calculating process performed by the solvingunit 112 according to this exemplary embodiment is hereinafterdescribed. FIG. 9 is a flowchart showing an operation of the estimateddistance calculating process performed by the solving unit 112. Arelaxed problem generating process performed by the constraint relaxingunit 101 according to this exemplary embodiment is similar to thatdescribed in the first exemplary embodiment.

Except for step S225, the estimated distance calculating processperformed by the solving unit 112 according to this exemplary embodimentis similar to that performed by the solving unit 102 according to thefirst exemplary embodiment. The set R of relaxed problems Q is inputtedto the solving unit 112 likewise (step S220). The solving unit 112calculates the transition array length for all of non-redundant paths πand returns, as the distance of the solution to the relaxed problem Q,the smallest value of the calculated transition array lengths (stepsS224 to S229).

As with the solving unit 102 according to the first exemplaryembodiment, the solving unit 112 calculates the transition array lengthby solving the relaxed problem Q having the non-redundant, fixed path πrelevant to the state element $Q (step S225). How to calculate thetransition array length is a distinction between the solving unit 112according to this exemplary embodiment and the solving unit 102according to the first exemplary embodiment.

Next, a transition array length calculating process performed by thesolving unit 112 according to this exemplary embodiment is hereinafterdescribed. FIG. 10 is a flowchart showing an operation of the transitionarray length calculating process performed by the solving unit 112.

After the non-redundant path π is fixed, the solving unit 112 sets thelength of π to SCORE[π] (step S240). Next, the solving unit 112retrieves, out of any state elements but the state element $Q includedin the relaxed problem Q, a state element E_i for which a state elementmodel M_i is yet to be generated. This means that the operation enters atransition array length calculating loop (step S241).

The solving unit 112, after retrieving the state element E_i, removesany state elements but the state element $Q and the state element E_ifrom the state element model indicated by the relaxed problem Q so as togenerate a new state element model M_i (step S242). Hereinafter, Q′refers to any problem expressed by the state element model M_i.

Then, the solving unit 112 obtains a transition array indicated by ashortest path on the state element model M_i for transition of the stateelement $Q along the path π from the current state to the target state(step S243).

Next, the solving unit 112 counts, among the transition arrays obtainedin step S243, the number of state transitions relevant to the stateelement E_i. Next, the solving unit 112 adds the number of counted statetransitions to SCORE[π] (step S244).

The solving unit 112 repeatedly executes steps S242 to S244 for anystate element E_i for which the state element model M_i is yet to begenerated among any state elements but the state elements $Q included inthe relaxed problem Q. Steps S242 to S244 are repeatedly performed foreach and all of any state elements E_i but the state element $Q includedin the relaxed problem Q.

After the state element models M_1, M_2, . . . , and M n are generatedin connection with the state elements E_1, E_2, . . . , and E_n otherthan the state element $Q included in the relaxed problem Q, the solvingunit 112 exits the transition array length calculating loop (step S245).

At the time of the solving unit 112 exiting the transition array lengthcalculating loop, the summed number of state transitions which areobtained in connection with the state element models, and path π lengthin total are stored in SCORE[π]. The solving unit 112 defines SCORE[π]at the time of exiting the transition array length calculating loop asthe distance of the solution to the relaxed problem Q when the path π isfixed. After the distance of the solution to the relaxed problem Q isobtained, the solving unit 112 proceeds to step S226.

Next, the transition array length calculating process performed by thesolving unit 112 is hereinafter described referring to FIG. 11. FIG. 11is an explanatory diagram showing an example of the transition arraylength calculating process performed by the solving unit 112.

In the transition array length calculating process showed in FIG. 11,the solving unit 112 handles the relaxed problem Q in which statetransition of the state element E1 is fixed to a non-redundant path“a₁→b₁→c₁”. The solving unit 112 divides the relaxed problem Q into aproblem Q′1 representing a state element model solely consisting ofstate elements E1 and E2, and a problem Q′2 representing a state elementmodel solely consisting of state elements E1 and E3 (step S242).

Next, the solving unit 112 obtains solutions to the problems Q′1 and Q′2(step S243). The solution to the problem Q′ 1 indicates that statetransition of the state element E2 occurs twice. The solution to theproblem Q′2 indicates that state transition of the state element E3occurs twice. Therefore, the length of the solution to the relaxedproblem Q is 2+2+2=6 (step S244).

Description of Effect

The solving unit 112 according to this exemplary embodiment divides therelaxed problem for different state elements and then solves the relaxedproblem by summing the solutions to the divided problems. In theestimated distance calculator 110 according to this exemplaryembodiment, the solving unit 112 further subdivides the relaxed problemthan in the first exemplary embodiment, which may allow the estimateddistance to be calculated at higher speeds. The estimated distancecalculator 110 according to this exemplary embodiment may beparticularly advantageous when handling problems seeking a shortest pathon a state element model including abundant state elements.

Third Exemplary Embodiment Description of Structure

A third exemplary embodiment of the present invention is hereinafterdescribed referring to the accompanying drawings.

FIG. 12 is a block diagram showing a configuration example of a thirdexemplary embodiment of an estimated distance calculator 120 accordingto the present invention. As showed in FIG. 12, the estimated distancecalculator 120 according to this exemplary embodiment has a constraintrelaxing unit 111 and a solving unit 122.

In the estimated distance calculator 120 according to this exemplaryembodiment, the constraint relaxing unit 101 and the solving unit 102according to the first exemplary embodiment are respectively replacedwith the constraint relaxing unit 111 and the solving unit 122.

The constraint relaxing unit 111 focuses on one state element $Qincluded in the state element model. The constraint relaxing unit 111traces “dependency destinations” included in the state element $Q oneafter another. By tracing the “dependency destinations”, the constraintrelaxing unit 111 selects dependencies originating from the stateelement $Q of interest alone. The constraint relaxing unit 111 deletesany dependencies but the selected dependencies from the state elementmodel.

In this manner, the constraint relaxing unit 111, while more carefullytaking into consideration dependency-related impacts than the constraintrelaxing unit 101 according to the first exemplary embodiment, generatesa more simplified relaxed problem than the original automated planningproblem.

The solving unit 122, before solving the relaxed problem Q, divides astate element model indicated by the relaxed problem Q for each one ofstate elements E_1, E_2, . . . , E_n which the state element $Q directlydepends upon. The solving unit 122, after dividing the state elementmodel indicated by the relaxed problem Q, obtains the length of atransition array.

Description of Operation

The operation to output the estimated distance obtained by an estimateddistance calculator 120 according to this exemplary embodiment ishereinafter described referring to FIGS. 13 and 19.

The description starts with a relaxed problem generating processperformed by the constraint relaxing unit 111. FIG. 13 is a flowchartshowing an operation of the relaxed problem generating process performedby the constraint relaxing unit 111.

After an automated planning problem P that seeks a shortest path on thestate element model M is inputted to the estimated distance calculator120, the automated planning problem P is inputted to the constraintrelaxing unit 111 (step S310). Then, the constraint relaxing unit 111defines a set R as void set (empty set) (step S311).

Next, the constraint relaxing unit 111 retrieves, out of the stateelements included in the state element model M, a state element E forwhich any relaxed problem Q relevant to itself is yet to be generated.This means that the operation enters a relaxed problem generating loop(step S312).

The constraint relaxing unit 111, on the basis of the retrieved stateelement E, generates a dependency tree T (E) relevant to the stateelement E (step S313). The dependency tree T (E) relevant to the stateelement E of the state element model M is a tree generated by connectingstate elements included in the state element model M with arrows.

However, the state elements E1 and E2 are connected with an arrow, like“E1→E2”, in the dependency tree T (E) only when dependency on the stateof the state element E2 is associated with state transition of the stateelement E1 included in the state element model M.

The constraint relaxing unit 111 generates the relaxed problem Qrelevant to the retrieved state element E (step S314). Morespecifically, the constraint relaxing unit 111 generates the relaxedproblem Q relevant to the state element E by deleting, from dependenciesincluded in the state element model M, all of dependencies butdependencies having the same direction as arrows constituting thedependency tree T (E) calculated in step S313.

For example, dependency “having the same direction” as the “arrow E1→E2constituting the dependency tree T (E)” is “dependency on the state ofthe state element E2 associated with state transition of the stateelement E1”.

Next, the constraint relaxing unit 111 redefines the set R as a set towhich the relaxed problems Q have been added (step S315). This meansthat the constraint relaxing unit 111 adds the relaxed problems Qgenerated in step S314 to the elements of the set R.

The constraint relaxing unit 111 repeatedly executes steps S313 to S315for any state element E for which any relaxed problem Q relevant toitself is yet to be generated among the state elements included in thestate element model M. Steps S313 to S315 are repeatedly performed foreach and all of the state elements included in the state element modelM.

After the relaxed problems Q relevant to all of the state elementsincluded in the state element model M are generated, the constraintrelaxing unit 111 exits the relaxed problem generating loop (step S316).The constraint relaxing unit 111 that exited the relaxed problemgenerating loop outputs the set R (step S317). After the output of theset R, the constraint relaxing unit 111 ends the relaxed problemgenerating process.

In step S313, the constraint relaxing unit 111 obtains the dependencytree T (E) by providing arrows while tracing the state elements by, forexample, breadth first search. The breadth first search is an algorithmused for exhaustive scans of the diagram.

The constraint relaxing unit 111 according to this exemplary embodimentregards the relationship in the state element model, “dependency on thestate of the state element E2 is associated with state transition of thestate element E1” as “branch (arrow) is extending from the state elementE1 to the state element E2”.

The constraint relaxing unit 111 thus regards each relationship as“branch” and interprets the state element model M as one diagram. Theconstraint relaxing unit 111 is allowed to calculate the dependency treeT (E) by exhaustively scanning the diagram of the state element model Musing breadth first search, starting from the state element E.

FIG. 14 is an explanatory diagram showing an example of automatedplanning problem P inputted to the constraint relaxing unit 111. Asshowed in FIG. 14, the state element model M indicated by the automatedplanning problem P includes state elements E1 to E4.

The state element E1 includes state transitions associated withdependencies on the state of the state element E2 and on the state ofthe state element E3. The state elements E2 and E4 respectively includestate transitions associated with dependencies on states of the otherstate elements.

FIG. 15 is an explanatory diagram showing an example of a dependencytree calculating process performed by the constraint relaxing unit 111.FIG. 15 shows the dependency tree calculating process using the breadthfirst search. Also, the dependency tree calculating process showed inFIG. 15 is a calculating process relevant to the state element E1included in the state element model showed in FIG. 14.

Rectangular boxes of FIG. 15 painted in black each represent a stateelement. The constraint relaxing unit 111 appends, to the state elementE1 in the left dashed rectangle of FIG. 15, arrows which arerespectively directed toward the state element E2 and toward the stateelement E3, as showed in the center dashed rectangle of FIG. 15.

Similarly, the constraint relaxing unit 111 appends, to the stateelement E2 in the center dashed rectangle of FIG. 15, an arrow directedtoward the state element E4, as showed in the right dashed rectangle ofFIG. 15. A set of state elements and arrows showed in the right dashedrectangle of FIG. 15 constitutes the dependency tree T (E1) calculatedand obtained by the constraint relaxing unit 111.

The breadth first search is an algorithm used by the constraint relaxingunit 111 to calculate a dependency tree. The constraint relaxing unit111 according to this exemplary embodiment may use any suitablealgorithm but the breadth first search for dependency tree calculation.

Depending on what algorithm is used for calculation, differentdependency trees may be obtained from the same inputted information. Theconstraint relaxing unit 111 according to this exemplary embodiment mayuse any type of dependency tree to generate a relaxed problem.Therefore, such variability of the dependency tree finally obtainedshould not be a problem. The relaxed problem generating process usingdependency trees performed by the constraint relaxing unit 111 ishereinafter described referring to the drawings.

FIG. 16 is an explanatory diagram showing another example of automatedplanning problem P inputted to the constraint relaxing unit 111. Asshowed in FIG. 16, the state element model M indicated by the automatedplanning problem P includes a state element E1, a state element E2, anda state element E3.

FIG. 17 is an explanatory diagram showing an example of a dependencytree generated by the constraint relaxing unit 111. The dependency treeT (E1) showed in FIG. 17 is a dependency tree calculated in connectionwith the state element E1 included in the state element model M showedin FIG. 16.

Similarly, a dependency tree T (E2) and a dependency tree T (E3) showedin FIG. 17 are respectively a dependency tree calculated in connectionwith the state element E2 included in the state element model M showedin FIG. 16 and a dependency tree calculated in connection with the stateelement E3 included in the same state element model M.

FIG. 18 is an explanatory diagram showing an example of the relaxedproblem generating process performed by the constraint relaxing unit111. FIG. 18 shows a process performed by the constraint relaxing unit111 to generate three relaxed problems using the dependency trees T(E1), T (E2), and T (E3) showed in FIG. 17.

The constraint relaxing unit 111 relaxes the automated planning problemP that seeks the shortest path on the state element model M using therelaxed problem generating process. Specifically, the constraintrelaxing unit 111, when relaxing the automated planning problem P inconnection with the state element E1, first obtains the dependency treeT (E1), like the one showed in FIG. 17. Next, the constraint relaxingunit 111 generates a relaxed problem Q1 which is the automated planningproblem P from which all of dependencies but dependencies having thesame direction as arrows constituting the dependency tree T (E1) havebeen deleted.

To generate the relaxed problem Q1, the constraint relaxing unit 111deletes dependency “E1:{a₁→b₁}” associated with transition of the stateelement E2 from the state b₂ to the state a₂. This dependency is deletedbecause the dependency tree T (E1) does not include any arrow having thesame direction as “dependency on the state of the state element E1associated with state transition of the state element E2”, i.e., arrowdirected from the state element E2 toward the state element E1.

Similarly, the constraint relaxing unit 111, when relaxing the automatedplanning problem P in connection with the state elements E2 and E3,generates relaxed problems Q2 and Q3. The constraint relaxing unit 111outputs the generated relaxed problems Q1 to Q3.

Next, the estimated distance calculating process performed by thesolving unit 122 is hereinafter described. The estimated distancecalculating process performed by the solving unit 122 according to thisexemplary embodiment is similar to the estimated distance calculatingprocess showed in FIG. 9. The transition array length calculatingprocess in step S225 performed by the solving unit 122 according to thisexemplary embodiment is distinct from the transition array lengthcalculating process performed by the solving unit 112 according to thesecond exemplary embodiment.

The transition array length calculating process performed by the solvingunit 122 according to this exemplary embodiment is hereinafterdescribed. FIG. 19 is a flowchart showing an operation of the transitionarray length calculating process performed by the solving unit 122.

In the second exemplary embodiment, “the state element still includingdependency among the state elements included in the relaxed problem Q”is recited as the state element $Q. In this exemplary embodiment, “theroot of the dependency tree used to generate the relaxed problem Q” isrecited as the state element $Q. In the example showed in FIG. 17, theroot of the dependency tree T (E1) is the state element E1.

The constraint relaxing unit 111 generates the relaxed problem Q usingthe dependency tree T ($Q). Hereinafter, the “dependency tree T ($Q)”refers to a dependency tree used to generate the relaxed problem Q. Thetransition array length calculating process is hereinafter describedbased on the assumption that a non-redundant path π on the state element$Q is fixed.

After the non-redundant path π is fixed, the solving unit 122 sets thelength of π in SCORE[π] (step S340). Next, the solving unit 122retrieves, out of the “state elements with arrows directly extendingfrom the state element $Q in the dependency tree T ($Q)”, a stateelement E_i for which no subtree has been formed. This means that theoperation enters a first transition array length calculating loop (stepS341).

The solving unit 122 that retrieved the state element E_i then forms, inthe dependency tree T ($Q), a subtree whose root is the state elementE_i. The solving unit 122 retrieves, out of the dependency tree T ($Q),any part reachable from the state element E_i along arrows as a subtree(step S342). A set of state elements included in the retrieved subtreeis hereinafter referred to as “U_i”.

The solving unit 122 that retrieved the subtree then removes any stateelements but the set U_i and the state element $Q from the state elementmodel indicated by the relaxed problem Q to generate a new state elementmodel M_i (step S343). Hereinafter, Q′ refers to any problem expressedby the state element model M_i.

Then, the solving unit 122 obtains the length of a transition array,which is the solution to the problem Q′, indicated by the shortest pathon the state element model M_i for state transition of the state element$Q along the path π from the current state to the target state (stepS344).

Then, the solving unit 122 adds, to SCORE[π], a value obtained bysubtracting the length of the fixed path π from the transition arraylength obtained in step S344 (step S345).

The solving unit 122 repeatedly executes steps S342 to S345 for anystate element E_i for which no subtree has been formed among the stateelements with arrows directly extending from the state element $Q in thedependency tree T ($Q). Steps S342 to S345 are repeatedly performed foreach and all of the state elements E_i with arrows directly extendingfrom the state element $Q in the dependency tree T ($Q).

The solving unit 122 exits the first transition array length calculatingloop after the subtrees are formed in connection with all of the stateelements E_i with arrows directly extending from the state element $Q inthe dependency tree T ($Q) (step S346).

Next, the solving unit 122 retrieves, out of “any state elements but thestate elements constituting the dependency tree T ($Q) included in thestate element model indicated by the relaxed problem Q”, a state elementF_i for which a transition array length is yet to be calculated. Thismeans that the operation enters a second transition array lengthcalculating loop (step S347).

The retrieved state element F_i is a state element in which all ofdependencies have been removed from the state transitions by theconstraint relaxing unit 111. None of the state elements indicated bythe relaxed problem Q includes dependency on the state element F_i.Therefore, the solving unit 122 may allow any optional state transitionof the state element F_i in connection with the relaxed problem Q.

Then, the solving unit 122 obtains a transition array indicated by theshortest path on the state element model indicated by the relaxedproblem Q for transition of the state element F_i from the current stateto the target state (step S348). The solving unit 122 may accordinglyeasily obtain the shortest path for transition of the state element F_ifrom the current state to the target state.

Next, the solving unit 122 adds, to SCORE[π], the length of thetransition array indicated by the shortest path obtained in step S348(step S349).

The solving unit 122 repeatedly executes steps S348 and S349 for anystate element F_i for which a transition array length is yet to becalculated among any state elements but the state elements constitutingthe dependency tree T ($Q). Steps S348 and S349 are repeatedly performedfor each and all of any state elements F_i but the state elementsconstituting the dependency tree T ($Q) in the state element modelindicated by the relaxed problem Q.

The solving unit 122 exits the second transition array lengthcalculating loop after the transition array lengths are calculated inconnection with all of the state elements F_i but the state elementsconstituting the dependency tree T ($Q) (step S350).

The solving unit 122 defines SCORE[π] at the time of exiting the secondtransition array length calculating loop as the distance of the solutionto the relaxed problem Q when the path π is fixed. After the distance ofthe solution to the relaxed problem Q is obtained, the solving unit 122proceeds to step S226.

Next, the transition array length calculating process performed by thesolving unit 122 is hereinafter described referring to the drawing. FIG.20 is an explanatory diagram showing the relaxed problem Q inputted tothe solving unit 122 and an example of the dependency tree T (E1) usedto generate the relaxed problem Q.

The relaxed problem Q showed in FIG. 20 is a problem relaxed along thedependency tree T (E1). In the state element E1, dependency “E2: {a₂}”is associated with the state transition from a₁ to c₁, and dependencies“E2: {a₂}” and “E3: {a₃}” are associated with the state transition fromb₁ to c₁, as showed in FIG. 20. In the state element E2, dependency“E4:{a₄}” is associated with the state transition from b₂ to a₂.

In the dependency tree T (E1) showed in FIG. 20, arrows are extendingfrom the state element E1 to the state element E2 and from the stateelement E1 to the state element E3. Also, an arrow is extending from thestate element E2 to the state element E4. The state element E5 is notincluded in the dependency tree T (E1).

FIG. 21 is an explanatory diagram showing a process to calculate thedistance of the solution to the relaxed problem Q in the transitionarray length calculating process performed by the solving unit 122. Inthe transition array length calculating process showed in FIG. 21, thesolving unit 122 handles the relaxed problem Q in which state transitionof the state element E1 is fixed to a non-redundant path π=“a₁→b₁→c₁”.

In the transition array length calculating process showed in FIG. 21,the solving unit 122 generates a subtree T1 whose root is the stateelement E2 with an arrow directly extending from the state element E1which is the root of the dependency tree T (E1), and also generates asubtree T2 whose root is the state element E3 with an arrow directlyextending from the state element E1 (step S342).

FIG. 22 is an explanatory diagram showing an example of subtreesgenerated by the solving unit 122. The subtrees showed in FIG. 22 areeach obtained by selecting one branch from the dependency tree in astage of the transition array length calculating process performed bythe solving unit 122.

The subtree T1 of FIG. 22 is generated when the state element E2 isselected as root. The subtree T1 includes the state elements E2 and E4.An arrow is extending from the state element E2 to the state element E4.

The subtree T2 of FIG. 22 is generated when the state element E3 isselected as root. The subtree T2 includes the state element E3 alone,i.e., one node. The subtree T2 has no arrow.

Next, the solving unit 122 restricts the state element model indicatedby the relaxed problem Q using the state elements included in thesubtrees T1 and T2 (step S343).

FIG. 23 is an explanatory diagram showing an example of the problem Q′generated by the solving unit 122. FIG. 23 shows a problem restricted bythe use of subtrees in a stage of the transition array lengthcalculating process performed by the solving unit 122.

A problem Q′1 showed in FIG. 23 is a problem in which the state elementmodel indicated by the relaxed problem Q is restricted to the subtreeT1. The state element model indicated by the problem Q′1 includes thestate elements E1, E2, and E4 alone.

A problem Q′2 showed in FIG. 23 is a problem in which the state elementmodel indicated by the relaxed problem Q is restricted to the subtreeT2. The state element model indicated by the problem Q′2 includes thestate elements E1 and E3 alone. The state element models respectivelyindicated by the problem Q′1 and the problem Q′ 2 both include the stateelement E1, which is the state element $Q, in addition to elements ofthe subtrees.

Next, the solving unit 122 obtains solutions to the problems Q′1 and Q′2(step S344). In step S344, the solving unit 122 elicits shortest pathson the respective state element models indicated by the defined problemsQ′1 and Q′2 that are provided by defining the subtrees. The problems aresolved by the transition array length calculating process internally andrecursively performed by the solving unit 122.

An example of how the problem Q′1 is solvable by the solving unit 122according to this method is hereinafter described. FIG. 24 is anexplanatory diagram showing an example of how the problem Q′ is solvedby the solving unit 122. FIG. 24 shows a process to solve a problemrestricted by the use of subtrees in a stage of the transition arraylength calculating process performed by the solving unit 122. In theexample showed in FIG. 24, the solving unit 122 recursively uses thetransition array length calculating process internally so as tocalculate the distance of the solution to the problem Q′ 1.

As for the problem Q′1, state transition of the state element E1 alongthe fixed path π requires state transition of the state element E2 toa₂. The solving unit 122 accordingly lists up non-redundant paths thatmay allow transitions of the state element E2 to a₂ and then to thetarget state b₂.

The solving unit 122 presents π′=“b₂→a₂→b₂” showed in FIG. 24 as theonly path meeting the requirement. Therefore, the distance of thesolution to the problem Q′1 to be determined is a value obtained byadding the π length “2” to the distance of the solution to a problem Q″1in which the problem Q′1 is restricted to the state elements E2 and E4and state transition of the state element E2 is fixed to a path π′ andexecuted.

The solution to the problem Q″1 is obtainable in a similar manner. Thedistance of the solution to the problem Q″1 is a value obtained byadding the π′ length “2” to the distance of the solution to a problemQ′″1 in which the problem Q″1 is restricted to the state element E4alone and state transition of the state element E4 is fixed to a path π″=“b₄→a₄→b₄” and executed.

Because of no dependency being included in the problem Q′″1, the solvingunit 122 may immediately determine that the distance of the solution tothe problem Q′″1 is equal to the π′ length “2”. Thus, the solving unit122 may recursively calculate the distance of the solution to theoriginal problem Q′1 as “2+2+2=6”.

By thus subdividing the problem into problems including no dependency atall, the solving unit 122 may obtain the transition array length usingthe transition array length calculating process of step S344.

The above-described method that is employed by the solving unit 122 torecursively use the transition array length calculating process is onemethod that can be employed by the solving unit 122 to obtain, in stepS344, the transition array length indicative of the shortest path. Thesolving unit 122 according to this exemplary embodiment may employ anysuitable method, instead of the method described above, to obtain thetransition array length indicative of the shortest path.

In a similar manner, the solving unit 122 calculates and obtains “4” asthe distance of the solution to the problem Q′2. After the distances ofthe solutions to the problems Q′1 and Q′2 are obtained, the solving unit122 adds, to SCORE[π] (initial value is the π length “2”), valuesobtained by subtracting the path π length “2” from the respectivedistances (step S345).

After the distances of the solutions to the problems Q′1 and Q′2 areobtained, the solving unit 122 enters the second transition array lengthcalculating loop (steps S346 and S347). In the state element modelindicated by the relaxed problem Q, the state element E5 alone is notincluded in the dependency tree T (E1).

Therefore, the solving unit 122 obtains the transition array length “F”indicative of the shortest path for transition of the state element E5from the current state to the target state (step S348). Next, thesolving unit 122 adds the obtained transition array length to SCORE[π](step S349).

After the transition array length is added, the solving unit 122 exitsthe second transition array length calculating loop (step S350). Then,the solving unit 122 outputs SCORE[π]=2+4+2+1=9 as the distance of thesolution to the relaxed problem Q when state transition of the stateelement E1 showed in FIG. 20 is fixed to the path π, and then ends thetransition array length calculating process.

Description of Effect

The constraint relaxing unit 111 according to this exemplary embodimentgenerates the relaxed problem on which more dependencies are reflectedthan the relaxed problem generated by the constraint relaxing unit 101according to the first exemplary embodiment. The estimated distancecalculator 120 according to this exemplary embodiment, therefore, maymore accurately calculate the estimated distance than the estimateddistance calculator 100 according to the first exemplary embodiment.

Because more dependencies are reflected on the relaxed problem accordingto this exemplary embodiment, the resulting relaxed problem may becomplicated relative to the relaxed problem generated in the firstexemplary embodiment. The solving unit 122, however, further subdividesthe relaxed problem generated by the use of the dependency tree, whichmay allow solving unit 122 to obtain the solution with less time thanrequired to solve the original automated planning problem.

Fourth Exemplary Embodiment Description of Structure

A fourth exemplary embodiment of the present invention is hereinafterdescribed referring to the accompanying drawings. The fourth exemplaryembodiment represents an exemplary embodiment to which the first,second, and third exemplary embodiments are applied.

FIG. 25 is a block diagram showing a configuration example of a fourthexemplary embodiment of an automated planner 200 according to thepresent invention. As showed in FIG. 25, the automated planner 200according to this exemplary embodiment has an estimated distancecalculation unit 201, a shortest path searching unit 202, an inputcombining unit 203, and a converter 204.

The automated planner 200 according to this exemplary embodimentreceives, as input, a state element model M, and then conducts the A*search so as to obtain the solution to an automated planning problemrepresenting a shortest path on the state element model M. The automatedplanner 200 conducts the A* search in order to obtain a shortest path ona global state diagram on which the inputted state element model M islaid out.

The estimated distance calculation unit 201 is functionally andstructurally similar to the estimated distance calculator 100 describedin the first exemplary embodiment, the estimated distance calculator 110described in the second exemplary embodiment, and the estimated distancecalculator 120 described in the third exemplary embodiment.

The shortest path searching unit 202 has a function to search theshortest path on the state element model M. The shortest path searchingunit 202 conducts the A* search to search the shortest path on theinputted global state diagram.

The A* search requires an estimated distance from the current state tothe target state at an intermediate point during the ongoing search.When the estimated distance is requested, the shortest path searchingunit 202 makes an inquiry with the estimated distance calculation unit201 about the estimated distance through the input combining unit 203.The shortest path searching unit 202 uses, as the estimated distance, avalue returned from the estimated distance calculation unit 201.

The input combining unit 203 has a function to combine global states andthe state element model M. The input combining unit 203 inputs theglobal states and state element model M thus combined to the estimateddistance calculation unit 201.

For example, the state element model M and global states G which areconversion results of the state element model M are inputted to theinput combining unit 203. The input combining unit 203 generates a stateelement model M′ in which the initial state of the state element model Mhas been reset to the global state G, and outputs the generated stateelement model M′.

Each global state retains three values; “search-completed” flag,shortest distance, and score. In the global initial state, the“search-completed” flag is set, and “0” is set as values of the shortestdistance, while no value is set as the score.

The converter 204 has a function to convert the inputted state elementmodel M into a global state diagram. The converter 204 may, for example,convert the state element model M into the global state diagram in amanner similar to the method described in PTL 1.

Description of Operation

The shortest path searching process performed by the shortest pathsearching unit 202 according to this exemplary embodiment is hereinafterdescribed. FIG. 26 is a flowchart showing an operation of the shortestpath searching process performed by the shortest path searching unit202.

First, the state element model M and the global state diagram on whichthe state element model M is laid out are inputted to the shortest pathsearching unit 202 (step S400). Then, the shortest path searching unit202 performs initial setting; set a current state C as the globalinitial state and 0 as the number of movements N (step S401). Theshortest path searching unit 202 proceed with the search, retaining onecurrent state C and the number of movements N.

Then, the shortest path searching unit 202 retrieves, out of globalstates allowed to transit from the current state C, any global state Swhose score is yet to be calculated. This means that the operationenters a score calculating loop (step S402).

After the global state S is retrieved, the input combining unit 203combines the global state S with the state element model M indicated bythe original automated planning problem so as to generate a stateelement model M′ (step S403). The input combining unit 203 inputs thegenerated state element model M′ to the estimated distance calculationunit 201.

The estimated distance calculation unit 201 calculates an estimateddistance E from the global state S to a global target state (step S404).Then, the shortest path searching unit 202 sets N+E+1 as the score ofthe global state S and sets N+1 as the shortest distance to the globalstate S (step S405).

The shortest path searching unit 202 repeatedly performs steps S403 toS405 for any global state S whose score is yet to be calculated amongthe global states allowed to transit from the current state C. StepsS403 to S405 are repeatedly performed for each and all of thescore-uncalculated global states S among the global states to whichtransition from the current state C is possible.

After the scores of all of the global states S allowed to transit fromthe current state C are calculated, the shortest path searching unit 202exits the score calculating loop (step S406).

Next, the shortest path searching unit 202 updates, among thescore-calculated global states yet to be searched, the global state witha lowest score to a new current state C. The shortest path searchingunit 202 further updates the number of movements N to a moving distanceto the new current state C (step S407).

In case there is no global state selectable as the current state C instep S407, the shortest path searching unit 202 ends the shortest pathsearching process. The shortest path searching unit 202 also sets the“search-completed” flag in the new current state C (step S408).

Next, the shortest path searching unit 202 determines whether thecurrent state C is the global target state (step S409). When the currentstate C is not the global target state (No in step S409), the shortestpath searching unit 202 executes step S402 again.

When the current state C is the global target state (Yes in step S409),the shortest path searching unit 202 outputs, as the shortest path, apath followed for the global initial state to arrive at the currentstate C (step S410). After the path is outputted, the shortest pathsearching unit 202 ends the shortest path searching process.

It is a known matter that the algorithm showed in FIG. 26 allows theshortest path to be correctly obtained when a heuristic function usedfor the search has consistency. The estimated distance calculation unit201 according to this exemplary embodiment functions as a heuristicfunction having consistency. The shortest path searching unit 202, byexecuting the process described earlier, returns the shortest path fromthe global initial state to the global target state.

The shortest path searching process performed by the shortest pathsearching unit 202 is hereinafter described referring to FIGS. 27 and28. FIGS. 27 and 28 are explanatory diagrams showing specific examplesof the shortest path searching process performed by the shortest pathsearching unit 202.

FIGS. 27 and 28 show a process to search the shortest path on the globalstate diagram. Rectangles of FIG. 27 and rectangles of FIG. 28 each showthe global state diagram in a stage of the shortest path searchingprocess. The state diagram during the shortest path searching processchanges in the order of the upper rectangle of FIG. 27, the centerrectangle of FIG. 27, the lower rectangle of FIG. 27, the upperrectangle of FIG. 28, and the lower rectangle of FIG. 28.

Circles showed in FIGS. 27 and 28 each represent a global state.Specifically, FIGS. 27 and 28 are drawings of global states S0 to S7.The global state S0 is the initial state, and the global state S7 is thetarget state.

FIG. 29 is a drawing of the state element model M which is the origin ofthe global state diagrams showed in FIGS. 27 and 28. FIG. 29 is anexplanatory diagram showing another example of the state element model.The meanings of the notations showed in FIG. 29 are the same as thoseshowed in FIG. 40. In the shortest path searching process showed inFIGS. 27 and 28, the state element model M showed in FIG. 29 is inputtedto the shortest path searching unit 202.

The state element model M showed in FIG. 29 represents a task in which astatus of one application being operated to read a predeterminedconfiguration file is changed to a status of two applications beingoperated to read an updated configuration file. The task showed in FIG.29 takes a scale-out approach of the applications.

Since three state elements are included in the state element model, theglobal state is expressed by combined states of the three stateelements. The global state including states of a state element “Conf”, astate element “App1”, and a state element “App2” is expressed by[Conf:(Conf state), App1:(App1 state), App2:(App2 state)].

For example, the global initial state S0 is expressed by S0=[Conf:old,App1:on, App2:off], as showed in FIGS. 27 and 28. The combination ofstates representing a global state is described in a black part of thecircle.

The “search-completed” flag, shortest distance, and score retained bythe global state are described in each of the global states showed inFIGS. 27 and 28 in addition to the combination of states representingthe global state. The “search-completed” flag is described in the upperright of each circle, the shortest distance is described in the lowerleft of each circle, and the score is described in the lower right ofeach circle. Any blank space indicates that a value to be described inthe space is yet to be set or calculated.

The shortest path searching process performed by the shortest pathsearching unit 202 is hereinafter described referring to the flowchartof FIG. 26. First, the shortest path searching unit 202 calculates andobtains the estimated distance to the target state for each of twoglobal states allowed to transit from the global initial state S0;global state 51 (51=[Conf:old, App1:on, App2:on]), and global state S2(S2=[Conf:old, App1:off, App2:off]).

After the global state 51 and the state element model M are inputted tothe input combining unit 203, the input combining unit 203 generates astate transition model M′ showed in FIG. 30 (step S403). FIG. 30 is anexplanatory diagram showing another example of the state element model.The input combining unit 203 inputs the generated state element model M′to the estimated distance calculation unit 201.

The estimated distance calculation unit 201 obtains the estimateddistance “5” on the basis of the generated state element model M′ (stepS404). By summing this estimated distance and the moving distance, thescore of the global state S1 is “6”. Similarly, the score of the globalstate S2 is “4” (step S405).

After the scores are thus calculated for all of the global statesallowed to transit from the current state C (step S406), the shortestpath searching unit 202 updates the current state C to the global stateS2 which is an unsearched state with a lowest score (step S407).

The shortest path searching unit 202 sets the “search-completed” flag inthe global state S2 (step S408). The center rectangle of FIG. 27 shows aglobal state diagram updated by setting in this diagram shortestdistances and scores of the global states S1 and S2 and the“search-completed” flag of the global state S2.

Similarly, the shortest path searching unit 202 executes steps S403 toS405 again for the unsearched states allowed to transit from the globalstate S2, and then executes steps S407 and S408 of updating the currentstate C to a global state with a lowest score.

The shortest path searching unit 202 repeatedly executes the processshowed in FIG. 26 until the current state C is updated to the globaltarget state S7 (S7=[Conf:new, App1:on, App2:on]). The lower rectangleof FIG. 28 shows a global state diagram after the current state C isupdated to the global target state S7.

The shortest path finally obtained is a path for transition of theglobal state in the global state diagram in the order of [Conf:old,App1:on, App2:off] →[Conf:old, App1:off App2:off]→[Conf:new, App1:off,App2:off]→[Conf:new, App1:on, App2:off]→[Conf:new, App1:on, App2:on].This is a transition path of S0→S2→S4→S5→S7.

When transition of the state element E from the state s1 to the state s2is described as “E:s1→s2”, the solution to the automated planningproblem showed in FIG. 29 is found to be a procedure, “App1:on→off,Conf:old→new, App1:off→on, App2:off→on”, based on the before-mentionedpath.

Description of Effect

The automated planner 200 according to this exemplary embodiment mayenable a more accelerated search of a shortest path by using theestimated distance calculation unit 201 that functions as a heuristicfunction suitable for the state element model. The automated planner 200according to this exemplary embodiment may provide a suitable method forfinding the solution to an automated planning problem seeking a shortestpath on a state element model.

Hereinafter, a specific example of hardware configuration of theestimated distance calculators according to the exemplary embodiments.FIG. 31 is an explanatory diagram showing an example of a hardwareconfiguration of the estimated distance calculator according to thepresent invention. FIG. 31 is a drawing of a hardware configuration thatallows a computer to functionally operate the estimated distancecalculators according to the exemplary embodiments.

As showed in FIG. 31, the estimated distance calculator has a CPU(Central Processing Unit) 191, a ROM (Read Only Memory) 192, a RAM(Random Access Memory) 193, and an output device 194. These structuralelements are interconnected with a data bus 195 to allow them totransmit and receive data to and from one another. An example of theoutput device 194 is a display device.

The estimated distance calculators described in the exemplaryembodiments may be operated by the CPU 191 executing processes byrunning programs stored in the ROM 192. The constraint relaxing units101 and 111, solving units 102, 112, and 122 may be functional elementsoperated under programmed control by the CPU 191 executing processes.

Optionally, the structural units provided in the estimated distancecalculators according to the exemplary embodiments may be respectivelyconfigured as hardware circuits. For example, the constraint relaxingunits 101 and 111, solving units 102, 112, and 122 may be eachconfigured as LSI (Large Scale Integration). The constraint relaxingunit and the solving unit may be collectively configured as one LSI.

The automated planner 200 according to the fourth exemplary embodimentmay include hardware components configured as showed in FIG. 31.

Next, the summary of the present invention is described. FIG. 32 is ablock diagram schematically showing the estimated distance calculatoraccording to the present invention. An estimated distance calculator 10according to the present invention generates, on the basis of a firststate element model comprising multiple state elements, a second stateelement model which is another state element model, wherein the stateelements include multiple states and state transitions assigned withtransition conditions between the multiple states. The estimateddistance calculator 10 has a generation unit 11 (for example, constraintrelaxing unit 101) which generates the second state element model insuch a manner as to comprise any one state element among the multiplestate elements and state elements other than the one state element whichare selected from among the multiple state elements after transitionconditions satisfying predetermined condition are removed.

The estimated distance calculator thus characterized may enable ahigh-speed search of a shortest path on the state element model.

The estimated distance calculator 10 may further include an elicitationunit (for example, solving unit 102) which receives, as input, thesecond state element model generated and elicits, on the basis of acurrent state and a target state included in the second state elementmodel, a smallest number of transitions for the current state to arriveat the target state.

Of all of the state transitions included in the second state elementmodel, there may be a limited number of state transitions that can beused.

The estimated distance calculator thus further characterized maysuccessfully solve a relaxed problem.

The transition condition satisfying the predetermined condition may beall of transition conditions.

The estimated distance calculator thus further characterized maygenerate a most simplified relaxed problem.

The transition condition satisfying the predetermined condition may beany transition condition but a transition condition having arelationship with a transition condition included in any one stateelement among the multiple state elements.

The state element model and one of the plurality of state elements maybe inputted to the generation unit 11, and the generation unit 11 maygenerate a dependency tree whose root is one state element.Specifically, the dependency tree includes nodes including part or allof the plurality of state elements, one or more directional branchesrepresenting a relationship that the dependency destination of acondition for transition included in one of two of the nodes is theother one of the two nodes, and a root included in one of the nodes. Thegeneration unit 11 may generate a second state element model includingone of the plurality of state elements, and a state element from whichany condition for transition but a condition for transition along thedirectional branches of the dependency tree whose root is one of theplurality of state elements. The condition for transition includes adependency destination including a title indicating part or all of aplurality of states.

The estimated distance calculator thus further characterized may solve arelaxed problem using such a dependency tree.

The elicitation unit may generate a third state element model which is astate element model comprising a state element assigned with transitionconditions and a state element from which transition conditions has beenremoved, the state elements being included in the second state elementmodel inputted, and then elicit a smallest number of transitions usingthe third state element model generated.

The elicitation unit may generate a problem in which a restriction isimposed on a state transition usable in a relaxed problem expressed bythe inputted second state element model, generate a third state elementmodel on the basis of a state element model that expresses the generatedproblem, and sum solutions to problems expressed by the third stateelement model to elicit a smallest number of transitions.

The estimated distance calculator thus further characterized may solveat high speed any relaxed problem including abundant state elements.

The elicitation unit may generate a third state element model which is astate element model comprising a group of relevant state elements amongmultiple state elements included in the second state element modelinputted, and elicit a smallest number of transitions using the thirdstate element model generated.

The elicitation unit may receive, as input, the dependency tree used togenerate the second state element model and generates a plurality ofdependency trees whose roots are nodes at which the roots of theinputted dependency tree arrive through one directional branch and whosenoses are part of state elements included in the dependency tree. Theelicitation unit may further generate a third state element modelincluding one or more of state element included in one of the pluralityof dependency trees among a plurality of state elements included in theinputted second state element model and elicit a smallest number oftransitions using the generated third state element model.

The estimated distance calculator thus further characterized may solve arelaxed problem including abundant state elements at high speed usingsubtrees.

The generation unit 11 may generate all of the second state elementmodels generatable based on the first state element model. Theelicitation unit may receive, as input, the all of the second stateelement models generated and elicit a smallest number of transitions onthe basis of and for each of the all of the second state element modelsinputted, and output a largest number of transitions among the elicitedsmallest numbers of transitions.

This may allow the estimated distance calculator to calculate anestimated distance including, as additional factor, dependency in astate element most affected by dependency between the state elements.The reason for that is, more constraints may be imposed on the relaxedproblem as the state elements are more affected by dependency, which maylead to longer distance of a solution to the relaxed problem.

The estimated distance calculator 10 may include a searching unit (forexample, shortest path searching unit 202) that searches, using thelargest number of transitions outputted by the elicitation unit as theestimated distance to the target state, a shortest path which is thesolution to the automated planning problem expressed by the first stateelement model.

This may allow the estimated distance calculator to solve the automatedplanning problem at high speed.

The elicitation unit may elicit a smallest number of transitions throughthe breadth first search.

The estimated distance calculator thus further characterized may solvethe automated planning problem at high speed using the breadth firstsearch.

The elicitation unit may repeatedly apply a transition array lengthcalculating process to the third state element model so as to elicit asmallest number of transitions.

The estimated distance calculator thus further characterized may solve arelaxed problem including abundant dependencies at high speed.

FIG. 33 is a block diagram schematically showing the automated planneraccording to the present invention. An automated planner 20 according tothe present invention generates, on the basis of a first state elementmodel comprising multiple state elements, a second state element modelwhich is another state element model, wherein the state elements includemultiple states and state transitions assigned with transitionconditions between the multiple states. The automated planner 20 has agenerator 21 (for example, estimated distance calculation unit 201), anelicitor 22 (for example, estimated distance calculation unit 201), anda searcher 23 (shortest path searching unit 202). The generator 21generates the second state element model in such a manner as to compriseany one state element among the multiple state elements and stateelements other than the one state element which are selected from amongthe multiple state elements after transition conditions satisfyingpredetermined condition are removed. The elicitor 22 receives, as input,the second state element model and elicits, on the basis of a currentstate and a target state included in the second state element model, asmallest number of transitions for the current state to arrive at thetarget state. The searcher 23 searches, using the smallest number oftransitions, a shortest path which is a solution to an automatedplanning problem expressed by the first state element model.

The automated planner thus characterized may enable a high-speed searchof the shortest path on the state element model.

The transition condition satisfying the predetermined condition may beall of transition conditions.

The automated planner thus further characterized may generate a mostsimplified relaxed problem.

The transition condition satisfying the predetermined condition may beany transition condition but a transition condition having arelationship with a transition condition included in any one stateelement among the multiple state elements.

The automated planner thus further characterized may solve a relaxedproblem using such a dependency tree.

The exemplary embodiments, in part or in whole, may be described as inthe supplementary notes below, which, however, only represent someexamples.

Supplementary Note 1

Provided is an automated planning method usable in an automated plannerthat generates, on the basis of a first state element model comprisingmultiple state elements, a second state element model which is anotherstate element model, wherein the state elements include multiple statesand state transitions assigned with transition conditions between themultiple states. The automated planning method includes: generating thesecond state element model in such a manner as to comprise any one stateelement among the multiple state elements and state elements other thanthe one state element which are selected from among the multiple stateelements after transition conditions satisfying predetermined conditionare removed; receiving, as input, the second state element model andeliciting, on the basis of a current state and a target state includedin the second state element model, a smallest number of transitions forthe current state to arrive at the target state; and searching, usingthe smallest number of transitions, a shortest path which is a solutionto an automated planning problem expressed by the first state elementmodel.

Supplementary Note 2

Provided is an automated planning program executable in a computer thatgenerates, on the basis of a first state element model comprisingmultiple state elements, a second state element model which is anotherstate element model, wherein the state elements include multiple statesand state transitions assigned with transition conditions between themultiple states. The automated planning program prompts the computer toexecute processing steps of: generating the second state element modelin such a manner as to comprise any one state element among the multiplestate elements and state elements other than the one state element whichare selected from among the multiple state elements after transitionconditions satisfying predetermined condition are removed; receiving, asinput, the second state element model and eliciting, on the basis of acurrent state and a target state included in the second state elementmodel, a smallest number of transitions for the current state to arriveat the target state; and searching, using the smallest number oftransitions, a shortest path which is a solution to an automatedplanning problem expressed by the first state element model.

The present invention was thus far described referring to the exemplaryembodiments and examples, however, are not necessarily limited to theabove-described exemplary embodiments and examples. The technicalaspects and details may include various modifications that can begrasped by those skilled in the art within the scope of mattersdescribed herein.

This application claims priority to Japanese Patent Application No.2016-143311 filed on Jul. 21, 2016 and Japanese Patent Application No.2016-223322 filed on Nov. 16, 2016, entire contents of which areincorporated herein by reference.

INDUSTRIAL APPLICABILITY

The automated planning technique may be effectively used to calculatefuture actions in advance using artificial intelligence and to planprocedures for executing the calculated actions. The present inventionis directed to optimizing an automated planning problem that searches ashortest path on a state element model and may be useful in efforts tosolve at high speed any automated planning problem associated with asystem including a plurality of small-sized subsystems that interferewith other subsystems.

REFERENCE SIGNS LIST

-   10, 100, 110, 120 Estimated distance calculator-   11 Generation unit-   20 Automated planner-   21 Generator-   22 Elicitor-   23 Searcher-   101, 111 Constraint relaxing unit-   102, 112, 122 Solving unit-   191 CPU-   192 ROM-   193 RAM-   194 Output device-   195 Data path-   200 Automated planner-   201 Estimated distance calculation unit-   202 Shortest path searching unit-   203 Input combining unit-   204 Converter

What is claimed is:
 1. An estimated distance calculator that generates,on the basis of a first state element model comprising multiple stateelements, a second state element model which is another state elementmodel, wherein the state elements include multiple states and statetransitions assigned with transition conditions between the multiplestates, the estimated distance calculator comprising a generation unitwhich generates the second state element model in such a manner as tocomprise any one state element among the multiple state elements andstate elements other than the one state element which are selected fromamong the multiple state elements after transition conditions satisfyingpredetermined condition are removed.
 2. The estimated distancecalculator according to claim 1, further comprising an elicitation unitwhich receives, as input, the second state element model generated andelicits, on the basis of a current state and a target state included inthe second state element model, a smallest number of transitions for thecurrent state to arrive at the target state.
 3. The estimated distancecalculator according to claim 2, wherein the transition conditionsatisfying the predetermined condition is all of transition conditions.4. The estimated distance calculator according to claim 2, wherein thetransition condition satisfying the predetermined condition is anytransition condition but a transition condition having a relationshipwith a transition condition included in any one state element among themultiple state elements.
 5. The estimated distance calculator accordingto claim 3, wherein the elicitation unit generates a third state elementmodel which is a state element model comprising a state element assignedwith transition conditions and a state element from which transitionconditions has been removed, the state elements being included in thesecond state element model inputted, and elicits a smallest number oftransitions using the third state element model generated.
 6. Theestimated distance calculator according to claim 4, wherein theelicitation unit generates a third state element model which is a stateelement model comprising a group of relevant state elements amongmultiple state elements included in the second state element modelinputted, and elicits a smallest number of transitions using the thirdstate element model generated.
 7. The estimated distance calculatoraccording to claim 2, wherein the generation unit generates all of thesecond state element models generatable based on the first state elementmodel, the elicitation unit receives, as input, the all of the secondstate element models generated, elicits a smallest number of transitionson the basis of and for each of the all of the second state elementmodels inputted, and outputs a largest number of transitions among theelicited smallest numbers of transitions.
 8. An estimated distancecalculation method usable in an estimated distance calculator thatgenerates, on the basis of a first state element model comprisingmultiple state elements, a second state element model which is anotherstate element model, wherein the state elements include multiple statesand state transitions assigned with transition conditions between themultiple states, the estimated distance calculation method comprising:generating the second state element model in such a manner as tocomprise any one state element among the multiple state elements andstate elements other than the one state element which are selected fromamong the multiple state elements after transition conditions satisfyingpredetermined condition are removed.
 9. A non-transitorycomputer-readable recording medium having recorded therein an estimateddistance calculation program executable in a computer that generates, onthe basis of a first state element model comprising multiple stateelements, a second state element model which is another state elementmodel, wherein the state elements include multiple states and statetransitions assigned with transition conditions between the multiplestates, the estimated distance calculation program prompting thecomputer to execute a processing step of generating the second stateelement model in such a manner as to comprise any one state elementamong the multiple state elements and state elements other than the onestate element which are selected from among the multiple state elementsafter transition conditions satisfying predetermined condition areremoved.
 10. An automated planner that generates, on the basis of afirst state element model comprising multiple state elements, a secondstate element model which is another state element model, wherein thestate elements include multiple states and state transitions assignedwith transition conditions between the multiple states, the automatedplanner comprising: a generator that generates the second state elementmodel in such a manner as to comprise any one state element among themultiple state elements and state elements other than the one stateelement which are selected from among the multiple state elements aftertransition conditions satisfying predetermined condition are removed; anelicitor that receives, as input, the second state element model andthat elicits, on the basis of a current state and a target stateincluded in the second state element model, a smallest number oftransitions for the current state to arrive at the target state; and asearcher that searches, using the smallest number of transitions, ashortest path which is a solution to an automated planning problemexpressed by the first state element model. 11-12. (canceled)
 13. Theestimated distance calculator according to claim 3, wherein thegeneration unit generates all of the second state element modelsgeneratable based on the first state element model, the elicitation unitreceives, as input, the all of the second state element modelsgenerated, elicits a smallest number of transitions on the basis of andfor each of the all of the second state element models inputted, andoutputs a largest number of transitions among the elicited smallestnumbers of transitions.
 14. The estimated distance calculator accordingto claim 4, wherein the generation unit generates all of the secondstate element models generatable based on the first state element model,the elicitation unit receives, as input, the all of the second stateelement models generated, elicits a smallest number of transitions onthe basis of and for each of the all of the second state element modelsinputted, and outputs a largest number of transitions among the elicitedsmallest numbers of transitions.
 15. The estimated distance calculatoraccording to claim 5, wherein the generation unit generates all of thesecond state element models generatable based on the first state elementmodel, the elicitation unit receives, as input, the all of the secondstate element models generated, elicits a smallest number of transitionson the basis of and for each of the all of the second state elementmodels inputted, and outputs a largest number of transitions among theelicited smallest numbers of transitions.
 16. The estimated distancecalculator according to claim 6, wherein the generation unit generatesall of the second state element models generatable based on the firststate element model, the elicitation unit receives, as input, the all ofthe second state element models generated, elicits a smallest number oftransitions on the basis of and for each of the all of the second stateelement models inputted, and outputs a largest number of transitionsamong the elicited smallest numbers of transitions.